arxiv: 2512.18274 · v2 · submitted 2025-12-20 · ✦ hep-ph · hep-th

Recognition: 2 theorem links

· Lean Theorem

High-Energy Pion Scattering in Holographic QCD: A Comparison with Experimental Data

Adi Armoni , Dorin Weissman

Authors on Pith no claims yet

Pith reviewed 2026-05-16 21:06 UTC · model grok-4.3

classification ✦ hep-ph hep-th

keywords holographic QCDhard-wall modelpion scatteringhigh-energy scatteringangular dependenceconstituent counting rulemeson scattering

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The pith

Holographic QCD hard-wall model predictions show qualitative agreement with data for high-energy fixed-angle pion scattering.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies the holographic hard-wall model to compute high-energy pion-pion scattering amplitudes. Building on earlier results that reproduce the constituent counting rule, it now compares the predicted angular dependence for π⁺π⁻ scattering to data extracted from π⁻p → π⁺π⁻n. The comparison reveals qualitative agreement in the high-energy fixed-angle regime. Predictions for other pion scattering channels are also given, with the method applicable to broader meson processes.

Core claim

Following the Polchinski-Strassler framework in the hard-wall holographic QCD model, the angular dependence of the high-energy π⁺π⁻ → π⁺π⁻ scattering amplitude qualitatively matches experimental data extracted from the π⁻p → π⁺π⁻n process, while also reproducing the constituent counting rule.

What carries the argument

The hard-wall holographic QCD model for computing meson scattering amplitudes at high energies via the Polchinski-Strassler approach.

If this is right

The model provides angular dependence predictions for all 2-to-2 pion scattering processes.
Qualitative agreement supports the holographic description of high-energy QCD scattering.
The approach extends to meson and glueball scattering in other holographic QCD models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the data extraction is accurate, the agreement implies holographic models can capture non-perturbative high-energy dynamics.
Future experiments could test the model by measuring other pion channels directly.
Similar comparisons might be made for baryon or glueball processes to broaden the validation.

Load-bearing premise

The extraction of the π⁺π⁻ scattering amplitude from π⁻p → π⁺π⁻n data introduces no significant background contamination.

What would settle it

A high-precision measurement showing a clear mismatch in the angular dependence of high-energy pion scattering compared to the holographic prediction.

read the original abstract

Following Polchinski and Strassler [1] and our previous work [2], we study high-energy pion scattering in the holographic QCD hard-wall model. In particular, we focus on comparing our predictions for the angular dependence of $\pi^{+} \pi^{-} \to \pi^{+} \pi^{-}$ scattering with experimental data extracted from the process $\pi^{-} p \to \pi^{+} \pi^{-} n$. Having previously shown that our approach reproduces the constituent counting rule found in QCD, we now observe qualitative agreement between our predictions and the extracted data in the high-energy fixed-angle regime. We also provide predictions for all other 2-to-2 pion scattering processes. Our approach can be extended to a broader range of meson and glueball scattering processes in various holographic QCD models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper checks hard-wall holographic predictions for high-energy pion angular distributions against data extracted from a three-body process and finds qualitative agreement.

read the letter

The main takeaway is that the hard-wall holographic QCD model from the authors' prior work produces angular dependence for π+π- scattering that lines up qualitatively with experimental points pulled from π-p → π+π-n in the fixed-angle high-energy regime. They also list predictions for the other pion channels. This is a direct, incremental step that tests the shape of the amplitude rather than just the overall power-law falloff already shown to match the constituent counting rule in their earlier paper. The calculation stays parameter-free beyond the choices fixed in the previous work, which keeps it clean and reproducible within the Polchinski-Strassler framework. For anyone already using hard-wall models to compute meson scattering, the comparison supplies a concrete benchmark that was missing before. The soft spot is the data extraction itself. The process is three-body, so residual t-channel backgrounds, nucleon resonances, or kinematic cuts could distort the angular region being tested. The abstract describes only qualitative agreement and does not mention error bands, fit statistics, or a re-derivation of the extraction procedure, so it is difficult to judge how robust the match actually is. If the full paper includes the plots and discusses the cuts in detail, that would address the main concern. This work is aimed at the narrow community already following holographic QCD phenomenology. Readers outside that group will not find it essential. It is worth sending to referees because the underlying calculation is grounded in an established model and the data comparison is a clear, falsifiable next step, even if the extraction step requires scrutiny during review.

Referee Report

2 major / 1 minor

Summary. The manuscript applies the holographic QCD hard-wall model, following Polchinski-Strassler and the authors' prior work, to high-energy pion scattering. It computes the angular dependence of π⁺π⁻ → π⁺π⁻ scattering and reports qualitative agreement with data extracted from π⁻p → π⁺π⁻n in the high-s, fixed-angle regime. Predictions are also given for the remaining 2-to-2 pion channels, with the approach positioned for extension to other mesons and glueballs.

Significance. If the qualitative agreement survives quantitative scrutiny and the amplitude extraction is shown to be free of significant kinematic contamination, the work would supply a direct experimental test of holographic predictions for high-energy meson scattering beyond the constituent counting rule already reproduced in the authors' earlier study. The absence of error bands, fit statistics, or cross-validation of the data extraction currently prevents a firm assessment of how much new support the comparison actually provides.

major comments (2)

Abstract: the central claim of 'qualitative agreement' between the hard-wall predictions and the extracted data is asserted without any accompanying plots, error bands, χ² values, or other quantitative measures, so the strength of the agreement cannot be evaluated from the manuscript as presented.
Data comparison section: the extraction of the π⁺π⁻ scattering amplitude from the three-body process π⁻p → π⁺π⁻n is not re-derived or validated inside the paper; residual one-pion-exchange backgrounds, nucleon resonances, or t-channel contamination that survive the cuts would directly distort the fixed-angle angular distributions used to test the holographic model.

minor comments (1)

The text should explicitly state which parameters and normalizations are taken unchanged from reference [2] versus which are newly constrained by the present data comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive suggestions. We have revised the manuscript to address the points raised and provide point-by-point responses below.

read point-by-point responses

Referee: Abstract: the central claim of 'qualitative agreement' between the hard-wall predictions and the extracted data is asserted without any accompanying plots, error bands, χ² values, or other quantitative measures, so the strength of the agreement cannot be evaluated from the manuscript as presented.

Authors: We agree that the abstract would benefit from greater precision. In the revised manuscript we have updated the abstract to explicitly reference Figure 3, which presents the angular distributions for π⁺π⁻ → π⁺π⁻ and allows direct visual assessment of the qualitative agreement. The holographic model is parameter-free once fixed by our earlier work, and the experimental extraction reported in the literature does not supply detailed uncertainties or fit statistics in the fixed-angle regime; therefore we have not added χ² values or error bands. A sentence has been added noting this limitation of the comparison. revision: yes
Referee: Data comparison section: the extraction of the π⁺π⁻ scattering amplitude from the three-body process π⁻p → π⁺π⁻n is not re-derived or validated inside the paper; residual one-pion-exchange backgrounds, nucleon resonances, or t-channel contamination that survive the cuts would directly distort the fixed-angle angular distributions used to test the holographic model.

Authors: The amplitude extraction is taken from the cited experimental analysis, which describes the kinematic cuts and background subtraction. We have added a concise summary of those procedures and the assumptions employed, together with a discussion of possible residual backgrounds. The original work argues that such contributions are suppressed in the high-s, fixed-angle region; we now explicitly note this claim and the associated caveat in the text. A full independent re-derivation lies beyond the scope of the present theoretical study, but the added discussion improves transparency regarding potential contamination. revision: partial

Circularity Check

0 steps flagged

Minor self-citation to prior model setup; central data comparison remains independent

full rationale

The derivation follows the standard hard-wall holographic QCD framework of Polchinski-Strassler [1] and applies the angular-dependence calculation developed in the authors' earlier paper [2]. The new element in this manuscript is the direct comparison of those fixed predictions against externally extracted experimental data from π⁻p → π⁺π⁻n. No equation in the present work re-derives or refits the model parameters inside the current text; the counting-rule reproduction is explicitly attributed to [2] rather than re-proven here. The qualitative agreement claim therefore rests on an external observable and does not collapse to a self-definitional loop or a fitted input renamed as a prediction within this paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract alone supplies insufficient detail on explicit parameters or new entities; the approach inherits the standard hard-wall cutoff and holographic dictionary from earlier literature.

axioms (1)

domain assumption The hard-wall holographic model approximates high-energy QCD scattering amplitudes
Invoked by reference to Polchinski-Strassler and prior work; no independent derivation supplied in abstract.

pith-pipeline@v0.9.0 · 5429 in / 1168 out tokens · 43144 ms · 2026-05-16T21:06:51.768263+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

A(s,t)∝ s²+st+t²/s³u ∫ dy y² B(−y,−(t/s)y) with hard-wall IR cutoff and PMA/1PE data extraction (eqs. 2.28, 4.1–4.2)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

High-energy fixed-angle limit yields s^{-2} scaling from UV AdS region only (eq. 2.21)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

53 extracted references · 53 canonical work pages · 18 internal anchors

[1]

Hard Scattering and Gauge/String Duality

J. Polchinski and M.J. Strassler,Hard scattering and gauge / string duality,Phys. Rev. Lett. 88(2002) 031601 [hep-th/0109174]. – 26 –

work page internal anchor Pith review Pith/arXiv arXiv 2002
[2]

Armoni, B

A. Armoni, B. Pyszkowski, S. Sugimoto and D. Weissman,High-energy fixed-angle meson scattering and the constituent counting rule in holographic QCD,JHEP05(2025) 221 [2412.17784]

work page arXiv 2025
[3]

The Large N Limit of Superconformal Field Theories and Supergravity

J.M. Maldacena,The LargeNlimit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231 [hep-th/9711200]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[4]

Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories

E. Witten,Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys.2(1998) 505 [hep-th/9803131]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[5]

Adding flavor to AdS/CFT

A. Karch and E. Katz,Adding flavor to AdS / CFT,JHEP06(2002) 043 [hep-th/0205236]

work page internal anchor Pith review Pith/arXiv arXiv 2002
[6]

Low energy hadron physics in holographic QCD

T. Sakai and S. Sugimoto,Low energy hadron physics in holographic QCD,Prog. Theor. Phys.113(2005) 843 [hep-th/0412141]

work page internal anchor Pith review Pith/arXiv arXiv 2005
[7]

Large N Field Theories, String Theory and Gravity

O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz,Large N field theories, string theory and gravity,Phys. Rept.323(2000) 183 [hep-th/9905111]

work page internal anchor Pith review Pith/arXiv arXiv 2000
[8]

Holographic QCD: Past, Present, and Future

Y. Kim, I.J. Shin and T. Tsukioka,Holographic QCD: Past, Present, and Future,Prog. Part. Nucl. Phys.68(2013) 55 [1205.4852]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[9]

Ammon and J

M. Ammon and J. Erdmenger,Gauge/gravity duality: Foundations and applications, Cambridge University Press, Cambridge (4, 2015), 10.1017/CBO9780511846373

work page doi:10.1017/cbo9780511846373 2015
[10]

Veneziano,Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories,Nuovo Cim

G. Veneziano,Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories,Nuovo Cim. A57(1968) 190

work page 1968
[11]

Green, J.H

M.B. Green, J.H. Schwarz and E. Witten,Superstring Theory, Vol. 1, Cambridge Monographs on Mathematical Physics, Cambridge University Press (7, 1988), 10.1017/CBO9781139248563

work page doi:10.1017/cbo9781139248563 1988
[12]

Matveev, R.M

V.A. Matveev, R.M. Muradian and A.N. Tavkhelidze,Automodellism in the large - angle elastic scattering and structure of hadrons,Lett. Nuovo Cim.7(1973) 719

work page 1973
[13]

Brodsky and G.R

S.J. Brodsky and G.R. Farrar,Scaling Laws at Large Transverse Momentum,Phys. Rev. Lett.31(1973) 1153

work page 1973
[14]

Brodsky and G.R

S.J. Brodsky and G.R. Farrar,Scaling Laws for Large Momentum Transfer Processes,Phys. Rev. D11(1975) 1309

work page 1975
[15]

T. Reed, C. Leon, F. Vera, L. Guo and B. Raue,Constituent counting rule andω photoproduction,Phys. Rev. C103(2021) 065203 [2005.13067]

work page arXiv 2021
[16]

Bromberg et al.,A Study of the Reactionπ −p→π +π−nat 100-GeV/cand 175-GeV/c, Nucl

C. Bromberg et al.,A Study of the Reactionπ −p→π +π−nat 100-GeV/cand 175-GeV/c, Nucl. Phys. B232(1984) 189

work page 1984
[17]

Martin, D

B.R. Martin, D. Morgan and G. Shaw,Pion Pion Interactions in Particle Physics, Academic Press (1976)

work page 1976
[18]

Stampke,Pion Pion Decay Distributions forπ −p→π +π−nat 100-GeV/c and 175-GeV/c, Ph.D

S.R. Stampke,Pion Pion Decay Distributions forπ −p→π +π−nat 100-GeV/c and 175-GeV/c, Ph.D. thesis, Caltech, 1982. 10.2172/1433900

work page doi:10.2172/1433900 1982
[19]

Bianchi, M

M. Bianchi, M. Firrotta, J. Sonnenschein and D. Weissman,Partonic behavior of string scattering amplitudes from holographic QCD models,JHEP05(2022) 058 [2111.12106]

work page arXiv 2022
[20]

A New Holographic Model of Chiral Symmetry Breaking

S. Kuperstein and J. Sonnenschein,A New Holographic Model of Chiral Symmetry Breaking, JHEP09(2008) 012 [0807.2897]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[21]

Son and M.A

D.T. Son and M.A. Stephanov,Qcd and dimensional deconstruction,Phys. Rev. D69(2004) 065020. – 27 –

work page 2004
[22]

The Pomeron and Gauge/String Duality

R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan,The Pomeron and gauge/string duality,JHEP12(2007) 005 [hep-th/0603115]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[23]

Hard Scattering in the M-Theory Dual for the QCD String

R.C. Brower and C.-I. Tan,Hard scattering in the M theory dual for the QCD string,Nucl. Phys. B662(2003) 393 [hep-th/0207144]

work page internal anchor Pith review Pith/arXiv arXiv 2003
[24]

Chiral perturbation theory

G. Ecker,Chiral perturbation theory,Prog. Part. Nucl. Phys.35(1995) 1 [hep-ph/9501357]

work page internal anchor Pith review Pith/arXiv arXiv 1995
[25]

Another look at $\pi\pi$ scattering in the scalar channel

K. Igi and K.-i. Hikasa,Another look at pi pi scattering in the scalar channel,Phys. Rev. D 59(1999) 034005 [hep-ph/9807326]

work page internal anchor Pith review Pith/arXiv arXiv 1999
[26]

Dai and J

J. Dai and J. Polchinski,The Decay of Macroscopic Fundamental Strings,Phys. Lett. B220 (1989) 387

work page 1989
[27]

Holographic decays of large-spin mesons

K. Peeters, J. Sonnenschein and M. Zamaklar,Holographic decays of large-spin mesons, JHEP02(2006) 009 [hep-th/0511044]

work page internal anchor Pith review Pith/arXiv arXiv 2006
[28]

Iengo and J.G

R. Iengo and J.G. Russo,Handbook on string decay,JHEP02(2006) 041 [hep-th/0601072]

work page arXiv 2006
[29]

The decay width of stringy hadrons

J. Sonnenschein and D. Weissman,The decay width of stringy hadrons,Nucl. Phys. B927 (2018) 368 [1705.10329]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[30]

Witten,Baryons in the 1/n Expansion,Nucl

E. Witten,Baryons in the 1/n Expansion,Nucl. Phys. B160(1979) 57

work page 1979
[31]

An Introduction to quantum field theory,

M.E. Peskin and D.V. Schroeder,An Introduction to quantum field theory, Addison-Wesley, Reading, USA (1995), 10.1201/9780429503559

work page doi:10.1201/9780429503559 1995
[32]

Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude

S. Caron-Huot, Z. Komargodski, A. Sever and A. Zhiboedov,Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude,JHEP10(2017) 026 [1607.04253]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[33]

Fredericksen,A Study of the Reactionπ −p→π +π−nat Beam Momenta of 100-GeV/c and 175-GeV/c, Ph.D

F.J. Fredericksen,A Study of the Reactionπ −p→π +π−nat Beam Momenta of 100-GeV/c and 175-GeV/c, Ph.D. thesis, Indiana U., 1982

work page 1982
[34]

Bromberg et al.,Highlights of the Reactionπ −p→π −π+nat 100-GeV/cand 175-GeV/c, Phys

C. Bromberg et al.,Highlights of the Reactionπ −p→π −π+nat 100-GeV/cand 175-GeV/c, Phys. Rev. D29(1984) 588

work page 1984
[35]

Bromberg et al.,NUMERICAL TABLES OF MEASUREMENTS FROM FERMILAB EXPERIMENT E110 FOR THE REACTIONS pi- p —>pi+ pi- n, pi- p —>A2- p, K- p —>K*- (980) p AND K- p —>K*- (1420) p,

C. Bromberg et al.,NUMERICAL TABLES OF MEASUREMENTS FROM FERMILAB EXPERIMENT E110 FOR THE REACTIONS pi- p —>pi+ pi- n, pi- p —>A2- p, K- p —>K*- (980) p AND K- p —>K*- (1420) p,

work page
[36]

Aderholz et al.,Investigation of exchange mechanisms inπ+p interactions at 4 GeV/c, in 12th International Conference on High Energy Physics, 1964

M. Aderholz et al.,Investigation of exchange mechanisms inπ+p interactions at 4 GeV/c, in 12th International Conference on High Energy Physics, 1964

work page 1964
[37]

Aderholz et al.,A study ofπ+p interactions at 4 GeV/c, in12th International Conference on High Energy Physics, 1964

M. Aderholz et al.,A study ofπ+p interactions at 4 GeV/c, in12th International Conference on High Energy Physics, 1964

work page 1964
[38]

Bondar et al.,π +pinteractions at 4 GeV/c: Six prong events,

L. Bondar et al.,π +pinteractions at 4 GeV/c: Six prong events,

work page
[39]

Hyams, W

B.D. Hyams, W. Koch, D.C. Potter, J.D. Wilson, L. von Lindern, E. Lorenz et al.,The Reactionπ −p→ρ 0nandK −p→K ∗0(890)nat 11.2 GeV/c,Nucl. Phys. B7(1968) 1

work page 1968
[40]

Robertson, W.D

W.J. Robertson, W.D. Walker and J.L. Davis,High-energy pi pi collisions,Phys. Rev. D7 (1973) 2554

work page 1973
[41]

Grayer et al.,High Statistics Study of the Reaction pi- p –>pi- pi+ n: Apparatus, Method of Analysis, and General Features of Results at 17-GeV/c,Nucl

G. Grayer et al.,High Statistics Study of the Reaction pi- p –>pi- pi+ n: Apparatus, Method of Analysis, and General Features of Results at 17-GeV/c,Nucl. Phys. B75(1974) 189. [42]Birmingham-Rutherford-Tel A viv-Westfieldcollaboration,New Data on the pi+ pi- Angular Distribution in the Mass Range 0.8-GeV/c**2 to 2.2-GeV/c**2,Nucl. Phys. B137 (1978) 221. – 28 –

work page 1974
[42]

Wicklund, D.S

A.B. Wicklund, D.S. Ayres, R. Diebold, A.F. Greene, S.L. Kramer and A.J. Pawlicki, Comparative Study of rho0, omega, K* (890) and anti-K* (890) Production by Charge Exchange,Phys. Rev. D17(1978) 1197

work page 1978
[43]

Weilhammer et al.,Elastic and totalπ +π− cross-sections from a high statistics measurement of the reactionπ −p→π +π−nat 63 GeV/c, in1979 EPS High-Energy Physics Conference, vol

P. Weilhammer et al.,Elastic and totalπ +π− cross-sections from a high statistics measurement of the reactionπ −p→π +π−nat 63 GeV/c, in1979 EPS High-Energy Physics Conference, vol. 2, (Geneva, Switzerland), pp. 628–635, CERN, 1979

work page 1979
[44]

Chew and F.E

G.F. Chew and F.E. Low,Unstable particles as targets in scattering experiments,Phys. Rev. 113(1959) 1640

work page 1959
[45]

Collins,An Introduction to Regge Theory and High Energy Physics, Cambridge University Press (1977), 10.1017/9781009403269

P.D.B. Collins,An Introduction to Regge Theory and High Energy Physics, Cambridge University Press (1977), 10.1017/9781009403269

work page doi:10.1017/9781009403269 1977
[46]

Mass spectra and Regge trajectories of light mesons in the relativistic quark model

D. Ebert, R.N. Faustov and V.O. Galkin,Mass spectra and Regge trajectories of light mesons in the relativistic quark model,Phys. Rev. D79(2009) 114029 [0903.5183]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[47]

Excited mesons, baryons, glueballs and tetraquarks: Predictions of the Holography Inspired Stringy Hadron model

J. Sonnenschein and D. Weissman,Excited mesons, baryons, glueballs and tetraquarks: Predictions of the Holography Inspired Stringy Hadron model,Eur. Phys. J. C79(2019) 326 [1812.01619]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[48]

Odorico,Evidence for veneziano dips in k- p scattering,Phys

R. Odorico,Evidence for veneziano dips in k- p scattering,Phys. Lett. B34(1971) 65

work page 1971
[49]

Odorico,Crucial tests of the veneziano model from dip behaviour at low energy,Nucl

R. Odorico,Crucial tests of the veneziano model from dip behaviour at low energy,Nucl. Phys. B37(1972) 509

work page 1972
[50]

Pennington,Zeros inππScattering,AIP Conf

M.R. Pennington,Zeros inππScattering,AIP Conf. Proc.13(1973) 89

work page 1973
[51]

Eguchi, T

T. Eguchi, T. Shimada and M. Fukugita,POLES AND ZEROS IN pi pi SCATTERING AMPLITUDES,Nucl. Phys. B74(1974) 102

work page 1974
[52]

A model for pion-pion scattering in large-N QCD

G. Veneziano, S. Yankielowicz and E. Onofri,A model for pion-pion scattering in large-N QCD,JHEP04(2017) 151 [1701.06315]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[53]

Guerrieri, K

A. Guerrieri, K. H¨ aring and N. Su,From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude,2410.23333. – 29 –

work page arXiv